Contradiction with James 1:13
Luke 4:13 suggests Jesus was tempted by the devil, while James 1:13 states that God cannot be tempted with evil.
James 1:13: Let no man say when he is tempted, I am tempted of God: for God cannot be tempted with evil, neither tempteth he any man: [evil: or, evils]
Contradiction with Hebrews 4:15
Luke 4:13 implies a conclusion to the temptation period, whereas Hebrews 4:15 indicates Jesus was tempted in all points throughout his life, suggesting ongoing temptation.
Hebrews 4:15: For we have not an high priest which cannot be touched with the feeling of our infirmities; but was in all points tempted like as [we are, yet] without sin.